Problem: All of William's friends wanted to try the candy bars he brought back from his trip, but there were only 20 candy bars. William decided to cut the candy bars into pieces so that each person could have $\frac{4}{5}$ of a candy bar. After cutting up the candy bars, how many friends could William share his candy with?
Explanation: We can divide the number of candy bars ( $20$ ) by the amount William gave to each person ( $\frac{4}{5}$ of a bar) to find out how many people he could share with. $ \dfrac{{20 \text{ candy bars}}} {{\dfrac{4}{5} \text{ bar per person}}} = {\text{ total people}} $ Dividing by a fraction is the same as multiplying by the reciprocal. The reciprocal of $\dfrac{4}{5} \text{ bar per person}$ is ${\dfrac{5}{4} \text{ people per bar}}$ $ {20\text{ candy bars}} \times {\dfrac{5}{4} \text{ people per bar}} = {\text{total people}} $ ${\dfrac{100}{4}\text{ people}} = 25\text{ people}$ By cutting up the candy bars, William could share his candy with 25 of his friends.